LMFDB - Embedded newform 966.2.i.m.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 10x^{5} + 47x^{4} + 180x^{3} + 220x^{2} + 768x + 1164 $ x^8 - 2x^7 + 13x^6 + 10x^5 + 47x^4 + 180x^3 + 220x^2 + 768*x + 1164
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$1.26426 - 2.63252i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.m.415.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.26426 - 2.18976i) q^{5} -1.00000 q^{6} +(-2.41196 - 1.08740i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.26426 - 2.18976i) q^{5} -1.00000 q^{6} +(-2.41196 - 1.08740i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.26426 + 2.18976i) q^{10} +(-2.14770 + 3.71993i) q^{11} +(0.500000 + 0.866025i) q^{12} +0.393417 q^{13} +(0.264260 + 2.63252i) q^{14} -2.52852 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.41196 + 5.90969i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +2.52852 q^{20} +(-2.14770 + 1.54512i) q^{21} +4.29540 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.696708 + 1.20673i) q^{25} +(-0.196708 - 0.340709i) q^{26} -1.00000 q^{27} +(2.14770 - 1.54512i) q^{28} +4.60658 q^{29} +(1.26426 + 2.18976i) q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.14770 + 3.71993i) q^{33} +6.82392 q^{34} +(0.668188 + 6.65638i) q^{35} +1.00000 q^{36} +(-4.52852 - 7.84363i) q^{37} +(1.00000 - 1.73205i) q^{38} +(0.196708 - 0.340709i) q^{39} +(-1.26426 - 2.18976i) q^{40} -3.05704 q^{41} +(2.41196 + 1.08740i) q^{42} +2.00000 q^{43} +(-2.14770 - 3.71993i) q^{44} +(-1.26426 + 2.18976i) q^{45} +(0.500000 - 0.866025i) q^{46} +(4.79540 + 8.30588i) q^{47} -1.00000 q^{48} +(4.63510 + 5.24555i) q^{49} +1.39342 q^{50} +(3.41196 + 5.90969i) q^{51} +(-0.196708 + 0.340709i) q^{52} +(-0.129157 + 0.223706i) q^{53} +(0.500000 + 0.866025i) q^{54} +10.8610 q^{55} +(-2.41196 - 1.08740i) q^{56} +2.00000 q^{57} +(-2.30329 - 3.98942i) q^{58} +(-5.05704 + 8.75905i) q^{59} +(1.26426 - 2.18976i) q^{60} +(-1.60658 - 2.78268i) q^{61} -2.00000 q^{62} +(0.264260 + 2.63252i) q^{63} +1.00000 q^{64} +(-0.497381 - 0.861490i) q^{65} +(2.14770 - 3.71993i) q^{66} +(-1.87084 + 3.24040i) q^{67} +(-3.41196 - 5.90969i) q^{68} +1.00000 q^{69} +(5.43050 - 3.90686i) q^{70} -13.8610 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.10658 + 3.64871i) q^{73} +(-4.52852 + 7.84363i) q^{74} +(0.696708 + 1.20673i) q^{75} -2.00000 q^{76} +(9.22523 - 6.63689i) q^{77} -0.393417 q^{78} +(-1.85230 - 3.20828i) q^{79} +(-1.26426 + 2.18976i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.52852 + 2.64748i) q^{82} -13.6478 q^{83} +(-0.264260 - 2.63252i) q^{84} +17.2544 q^{85} +(-1.00000 - 1.73205i) q^{86} +(2.30329 - 3.98942i) q^{87} +(-2.14770 + 3.71993i) q^{88} +(4.13510 + 7.16221i) q^{89} +2.52852 q^{90} +(-0.948906 - 0.427803i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(4.79540 - 8.30588i) q^{94} +(2.52852 - 4.37953i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(2.22523 - 6.63689i) q^{98} +4.29540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.26426	−	2.18976i	−0.565394	−	0.979292i	−0.997013	−	0.0772356i	$-0.975391\pi$
$5$	−1.26426	−	2.18976i	−0.565394	−	0.979292i	0.431618	−	0.902056i	$-0.357943\pi$
$6$	−1.00000			−0.408248
$7$	−2.41196	−	1.08740i	−0.911635	−	0.411000i
$7$	−2.41196	−	1.08740i	−0.911635	−	0.411000i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.26426	+	2.18976i	−0.399794	+	0.692464i
$11$	−2.14770	+	3.71993i	−0.647556	+	1.12160i	0.336149	+	0.941809i	$0.390875\pi$
$11$	−2.14770	+	3.71993i	−0.647556	+	1.12160i	−0.983705	+	0.179791i	$0.942458\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.393417			0.109114			0.0545571	−	0.998511i	$-0.482625\pi$
$13$	0.393417			0.109114			0.0545571	+	0.998511i	$0.482625\pi$
$14$	0.264260	+	2.63252i	0.0706265	+	0.703571i
$15$	−2.52852			−0.652861
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.41196	+	5.90969i	−0.827522	+	1.43331i	0.0724547	+	0.997372i	$0.476917\pi$
$17$	−3.41196	+	5.90969i	−0.827522	+	1.43331i	−0.899977	+	0.435938i	$0.856417\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	2.52852			0.565394
$21$	−2.14770	+	1.54512i	−0.468667	+	0.337172i
$22$	4.29540			0.915782
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.696708	+	1.20673i	−0.139342	+	0.241347i
$26$	−0.196708	−	0.340709i	−0.0385777	−	0.0668185i
$27$	−1.00000			−0.192450
$28$	2.14770	−	1.54512i	0.405877	−	0.292000i
$29$	4.60658			0.855421			0.427711	−	0.903916i	$-0.359320\pi$
$29$	4.60658			0.855421			0.427711	+	0.903916i	$0.359320\pi$
$30$	1.26426	+	2.18976i	0.230821	+	0.399794i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.14770	+	3.71993i	0.373867	+	0.647556i
$34$	6.82392			1.17029
$35$	0.668188	+	6.65638i	0.112944	+	1.12513i
$36$	1.00000			0.166667
$37$	−4.52852	−	7.84363i	−0.744484	−	1.28948i	−0.950435	−	0.310922i	$-0.899362\pi$
$37$	−4.52852	−	7.84363i	−0.744484	−	1.28948i	0.205951	−	0.978562i	$-0.433971\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$	0.196708	−	0.340709i	0.0314986	−	0.0545571i
$40$	−1.26426	−	2.18976i	−0.199897	−	0.346232i
$41$	−3.05704			−0.477430			−0.238715	−	0.971090i	$-0.576726\pi$
$41$	−3.05704			−0.477430			−0.238715	+	0.971090i	$0.576726\pi$
$42$	2.41196	+	1.08740i	0.372174	+	0.167790i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.14770	−	3.71993i	−0.323778	−	0.560800i
$45$	−1.26426	+	2.18976i	−0.188465	+	0.326431i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	4.79540	+	8.30588i	0.699481	+	1.21154i	0.968647	+	0.248443i	$0.0799187\pi$
$47$	4.79540	+	8.30588i	0.699481	+	1.21154i	−0.269166	+	0.963094i	$0.586748\pi$
$48$	−1.00000			−0.144338
$49$	4.63510	+	5.24555i	0.662158	+	0.749365i
$50$	1.39342			0.197059
$51$	3.41196	+	5.90969i	0.477770	+	0.827522i
$52$	−0.196708	+	0.340709i	−0.0272786	+	0.0472478i
$53$	−0.129157	+	0.223706i	−0.0177410	+	0.0307283i	−0.874760	−	0.484557i	$-0.838981\pi$
$53$	−0.129157	+	0.223706i	−0.0177410	+	0.0307283i	0.857019	+	0.515285i	$0.172314\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	10.8610			1.46450
$56$	−2.41196	−	1.08740i	−0.322312	−	0.145311i
$57$	2.00000			0.264906
$58$	−2.30329	−	3.98942i	−0.302437	−	0.523836i
$59$	−5.05704	+	8.75905i	−0.658371	+	1.14033i	0.322667	+	0.946513i	$0.395421\pi$
$59$	−5.05704	+	8.75905i	−0.658371	+	1.14033i	−0.981037	+	0.193819i	$0.937913\pi$
$60$	1.26426	−	2.18976i	0.163215	−	0.282697i
$61$	−1.60658	−	2.78268i	−0.205702	−	0.356286i	0.744654	−	0.667450i	$-0.232614\pi$
$61$	−1.60658	−	2.78268i	−0.205702	−	0.356286i	−0.950356	+	0.311164i	$0.899281\pi$
$62$	−2.00000			−0.254000
$63$	0.264260	+	2.63252i	0.0332937	+	0.331666i
$64$	1.00000			0.125000
$65$	−0.497381	−	0.861490i	−0.0616926	−	0.106855i
$66$	2.14770	−	3.71993i	0.264364	−	0.457891i
$67$	−1.87084	+	3.24040i	−0.228560	+	0.395877i	−0.957382	−	0.288826i	$-0.906735\pi$
$67$	−1.87084	+	3.24040i	−0.228560	+	0.395877i	0.728822	+	0.684704i	$0.240068\pi$
$68$	−3.41196	−	5.90969i	−0.413761	−	0.716655i
$69$	1.00000			0.120386
$70$	5.43050	−	3.90686i	0.649069	−	0.466959i
$71$	−13.8610			−1.64500			−0.822499	−	0.568766i	$-0.807421\pi$
$71$	−13.8610			−1.64500			−0.822499	+	0.568766i	$0.807421\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−2.10658	+	3.64871i	−0.246557	+	0.427049i	−0.962568	−	0.271040i	$-0.912633\pi$
$73$	−2.10658	+	3.64871i	−0.246557	+	0.427049i	0.716011	+	0.698089i	$0.245966\pi$
$74$	−4.52852	+	7.84363i	−0.526430	+	0.911803i
$75$	0.696708	+	1.20673i	0.0804490	+	0.139342i
$76$	−2.00000			−0.229416
$77$	9.22523	−	6.63689i	1.05131	−	0.756344i
$78$	−0.393417			−0.0445457
$79$	−1.85230	−	3.20828i	−0.208400	−	0.360959i	0.742811	−	0.669502i	$-0.233492\pi$
$79$	−1.85230	−	3.20828i	−0.208400	−	0.360959i	−0.951211	+	0.308542i	$0.900159\pi$
$80$	−1.26426	+	2.18976i	−0.141349	+	0.244823i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.52852	+	2.64748i	0.168797	+	0.292365i
$83$	−13.6478			−1.49805			−0.749023	−	0.662544i	$-0.769477\pi$
$83$	−13.6478			−1.49805			−0.749023	+	0.662544i	$0.769477\pi$
$84$	−0.264260	−	2.63252i	−0.0288332	−	0.287232i
$85$	17.2544			1.87151
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$	2.30329	−	3.98942i	0.246939	−	0.427711i
$88$	−2.14770	+	3.71993i	−0.228946	+	0.396545i
$89$	4.13510	+	7.16221i	0.438320	+	0.759193i	0.997560	−	0.0698131i	$-0.0222403\pi$
$89$	4.13510	+	7.16221i	0.438320	+	0.759193i	−0.559240	+	0.829006i	$0.688907\pi$
$90$	2.52852			0.266529
$91$	−0.948906	−	0.427803i	−0.0994724	−	0.0448460i
$92$	−1.00000			−0.104257
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$	4.79540	−	8.30588i	0.494608	−	0.856686i
$95$	2.52852	−	4.37953i	0.259421	−	0.449330i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	2.22523	−	6.63689i	0.224782	−	0.670427i
$99$	4.29540			0.431704
$100$	−0.696708	−	1.20673i	−0.0696708	−	0.120673i
$101$	−2.69671	+	4.67084i	−0.268333	+	0.464766i	−0.968431	−	0.249280i	$-0.919806\pi$
$101$	−2.69671	+	4.67084i	−0.268333	+	0.464766i	0.700099	+	0.714046i	$0.253139\pi$
$102$	3.41196	−	5.90969i	0.337834	−	0.585146i
$103$	9.07558	+	15.7194i	0.894244	+	1.54888i	0.834738	+	0.550648i	$0.185619\pi$
$103$	9.07558	+	15.7194i	0.894244	+	1.54888i	0.0595064	+	0.998228i	$0.481047\pi$
$104$	0.393417			0.0385777
$105$	6.09869	+	2.74952i	0.595171	+	0.268326i
$106$	0.258313			0.0250896
$107$	−8.29540	−	14.3681i	−0.801947	−	1.38901i	−0.918333	−	0.395808i	$-0.870465\pi$
$107$	−8.29540	−	14.3681i	−0.801947	−	1.38901i	0.116387	−	0.993204i	$-0.462869\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−7.28280	+	12.6142i	−0.697566	+	1.20822i	0.271742	+	0.962370i	$0.412400\pi$
$109$	−7.28280	+	12.6142i	−0.697566	+	1.20822i	−0.969308	+	0.245850i	$0.920933\pi$
$110$	−5.43050	−	9.40591i	−0.517778	−	0.896818i
$111$	−9.05704			−0.859656
$112$	0.264260	+	2.63252i	0.0249703	+	0.248750i
$113$	−9.11932			−0.857873			−0.428937	−	0.903335i	$-0.641112\pi$
$113$	−9.11932			−0.857873			−0.428937	+	0.903335i	$0.641112\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	1.26426	−	2.18976i	0.117893	−	0.204196i
$116$	−2.30329	+	3.98942i	−0.213855	+	0.370408i
$117$	−0.196708	−	0.340709i	−0.0181857	−	0.0314986i
$118$	10.1141			0.931077
$119$	14.6557	−	10.5438i	1.34349	−	0.966544i
$120$	−2.52852			−0.230821
$121$	−3.72523	−	6.45229i	−0.338657	−	0.586571i
$122$	−1.60658	+	2.78268i	−0.145453	+	0.251932i
$123$	−1.52852	+	2.64748i	−0.137822	+	0.238715i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−9.11932			−0.815657
$126$	2.14770	−	1.54512i	0.191332	−	0.137650i
$127$	6.27021			0.556391			0.278195	−	0.960524i	$-0.410264\pi$
$127$	6.27021			0.556391			0.278195	+	0.960524i	$0.410264\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	−0.497381	+	0.861490i	−0.0436232	+	0.0755577i
$131$	9.54915	+	16.5396i	0.834313	+	1.44507i	0.894588	+	0.446891i	$0.147469\pi$
$131$	9.54915	+	16.5396i	0.834313	+	1.44507i	−0.0602754	+	0.998182i	$0.519198\pi$
$132$	−4.29540			−0.373867
$133$	−0.528521	−	5.26504i	−0.0458286	−	0.456537i
$134$	3.74169			0.323233
$135$	1.26426	+	2.18976i	0.108810	+	0.188465i
$136$	−3.41196	+	5.90969i	−0.292573	+	0.506752i
$137$	8.76440	−	15.1804i	0.748793	−	1.29695i	−0.199608	−	0.979876i	$-0.563967\pi$
$137$	8.76440	−	15.1804i	0.748793	−	1.29695i	0.948401	−	0.317072i	$-0.102700\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	13.0413			1.10615			0.553073	−	0.833133i	$-0.313455\pi$
$139$	13.0413			1.10615			0.553073	+	0.833133i	$0.313455\pi$
$140$	−6.09869	−	2.74952i	−0.515433	−	0.232377i
$141$	9.59080			0.807691
$142$	6.93050	+	12.0040i	0.581595	+	1.00735i
$143$	−0.844941	+	1.46348i	−0.0706575	+	0.122382i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.82392	−	10.0873i	−0.483650	−	0.837707i
$146$	4.21317			0.348684
$147$	6.86033	−	1.39134i	0.565831	−	0.114756i
$148$	9.05704			0.744484
$149$	0.0311393	+	0.0539349i	0.00255103	+	0.00441852i	0.867298	−	0.497789i	$-0.165855\pi$
$149$	0.0311393	+	0.0539349i	0.00255103	+	0.00441852i	−0.864747	+	0.502208i	$0.832521\pi$
$150$	0.696708	−	1.20673i	0.0568860	−	0.0985295i
$151$	1.07806	−	1.86726i	0.0877315	−	0.151955i	−0.818820	−	0.574050i	$-0.805372\pi$
$151$	1.07806	−	1.86726i	0.0877315	−	0.151955i	0.906552	+	0.422094i	$0.138705\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	6.82392			0.551681
$154$	−10.3603	−	4.67084i	−0.834859	−	0.376387i
$155$	−5.05704			−0.406191
$156$	0.196708	+	0.340709i	0.0157493	+	0.0272786i
$157$	−5.54112	+	9.59750i	−0.442229	+	0.765964i	−0.997855	−	0.0654693i	$-0.979146\pi$
$157$	−5.54112	+	9.59750i	−0.442229	+	0.765964i	0.555625	+	0.831433i	$0.312479\pi$
$158$	−1.85230	+	3.20828i	−0.147361	+	0.255237i
$159$	0.129157	+	0.223706i	0.0102428	+	0.0177410i
$160$	2.52852			0.199897
$161$	−0.264260	−	2.63252i	−0.0208266	−	0.207472i
$162$	1.00000			0.0785674
$163$	−6.12721	−	10.6126i	−0.479920	−	0.831246i	0.519814	−	0.854279i	$-0.326001\pi$
$163$	−6.12721	−	10.6126i	−0.479920	−	0.831246i	−0.999735	+	0.0230329i	$0.992668\pi$
$164$	1.52852	−	2.64748i	0.119357	−	0.206733i
$165$	5.43050	−	9.40591i	0.422764	−	0.732249i
$166$	6.82392	+	11.8194i	0.529639	+	0.917362i
$167$	4.81975			0.372963			0.186482	−	0.982458i	$-0.440291\pi$
$167$	4.81975			0.372963			0.186482	+	0.982458i	$0.440291\pi$
$168$	−2.14770	+	1.54512i	−0.165699	+	0.119208i
$169$	−12.8452			−0.988094
$170$	−8.62721	−	14.9428i	−0.661677	−	1.14606i
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−11.4797	−	19.8833i	−0.872782	−	1.51170i	−0.859107	−	0.511796i	$-0.828980\pi$
$173$	−11.4797	−	19.8833i	−0.872782	−	1.51170i	−0.0136749	−	0.999906i	$-0.504353\pi$
$174$	−4.60658			−0.349224
$175$	2.99264	−	2.15299i	0.226222	−	0.162751i
$176$	4.29540			0.323778
$177$	5.05704	+	8.75905i	0.380111	+	0.658371i
$178$	4.13510	−	7.16221i	0.309939	−	0.536830i
$179$	−10.9226	+	18.9185i	−0.816394	+	1.41404i	0.0919281	+	0.995766i	$0.470697\pi$
$179$	−10.9226	+	18.9185i	−0.816394	+	1.41404i	−0.908322	+	0.418271i	$0.862636\pi$
$180$	−1.26426	−	2.18976i	−0.0942324	−	0.163215i
$181$	−22.0994			−1.64263			−0.821316	−	0.570473i	$-0.806760\pi$
$181$	−22.0994			−1.64263			−0.821316	+	0.570473i	$0.806760\pi$
$182$	0.103964	+	1.03568i	0.00770636	+	0.0767696i
$183$	−3.21317			−0.237524
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−11.4505	+	19.8328i	−0.841854	+	1.45813i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−14.6557	−	25.3845i	−1.07173	−	1.85630i
$188$	−9.59080			−0.699481
$189$	2.41196	+	1.08740i	0.175444	+	0.0790970i
$190$	−5.05704			−0.366876
$191$	4.13510	+	7.16221i	0.299206	+	0.518239i	0.975954	−	0.217975i	$-0.0699450\pi$
$191$	4.13510	+	7.16221i	0.299206	+	0.518239i	−0.676749	+	0.736214i	$0.736612\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	3.25375	−	5.63566i	0.234210	−	0.405664i	−0.724833	−	0.688925i	$-0.758083\pi$
$193$	3.25375	−	5.63566i	0.234210	−	0.405664i	0.959043	+	0.283261i	$0.0914163\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$	−0.994763			−0.0712364
$196$	−6.86033	+	1.39134i	−0.490024	+	0.0993816i
$197$	8.18025			0.582819			0.291409	−	0.956598i	$-0.405876\pi$
$197$	8.18025			0.582819			0.291409	+	0.956598i	$0.405876\pi$
$198$	−2.14770	−	3.71993i	−0.152630	−	0.264364i
$199$	7.20474	−	12.4790i	0.510731	−	0.884611i	−0.489192	−	0.872176i	$-0.662708\pi$
$199$	7.20474	−	12.4790i	0.510731	−	0.884611i	0.999923	−	0.0124352i	$-0.00395836\pi$
$200$	−0.696708	+	1.20673i	−0.0492647	+	0.0853290i
$201$	1.87084	+	3.24040i	0.131959	+	0.228560i
$202$	5.39342			0.379479
$203$	−11.1109	−	5.00922i	−0.779832	−	0.351578i
$204$	−6.82392			−0.477770
$205$	3.86490	+	6.69420i	0.269936	+	0.467543i
$206$	9.07558	−	15.7194i	0.632326	−	1.09522i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−0.196708	−	0.340709i	−0.0136393	−	0.0236239i
$209$	−8.59080			−0.594238
$210$	−0.668188	−	6.65638i	−0.0461093	−	0.459334i
$211$	15.1974			1.04623			0.523115	−	0.852262i	$-0.324770\pi$
$211$	15.1974			1.04623			0.523115	+	0.852262i	$0.324770\pi$
$212$	−0.129157	−	0.223706i	−0.00887051	−	0.0153642i
$213$	−6.93050	+	12.0040i	−0.474870	+	0.822499i
$214$	−8.29540	+	14.3681i	−0.567062	+	0.982180i
$215$	−2.52852	−	4.37953i	−0.172444	−	0.298681i
$216$	−1.00000			−0.0680414
$217$	−4.29540	+	3.09023i	−0.291591	+	0.209779i
$218$	14.5656			0.986507
$219$	2.10658	+	3.64871i	0.142350	+	0.246557i
$220$	−5.43050	+	9.40591i	−0.366124	+	0.634146i
$221$	−1.34232	+	2.32497i	−0.0902944	+	0.156394i
$222$	4.52852	+	7.84363i	0.303934	+	0.526430i
$223$	−21.1711			−1.41772			−0.708862	−	0.705348i	$-0.750791\pi$
$223$	−21.1711			−1.41772			−0.708862	+	0.705348i	$0.750791\pi$
$224$	2.14770	−	1.54512i	0.143499	−	0.103237i
$225$	1.39342			0.0928945
$226$	4.55966	+	7.89756i	0.303304	+	0.525338i
$227$	1.20474	−	2.08667i	0.0799615	−	0.138497i	−0.823272	−	0.567648i	$-0.807854\pi$
$227$	1.20474	−	2.08667i	0.0799615	−	0.138497i	0.903233	+	0.429150i	$0.141187\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	−5.30800	−	9.19372i	−0.350762	−	0.607538i	0.635621	−	0.772001i	$-0.280744\pi$
$229$	−5.30800	−	9.19372i	−0.350762	−	0.607538i	−0.986383	+	0.164463i	$0.947411\pi$
$230$	−2.52852			−0.166726
$231$	−1.13510	−	11.3077i	−0.0746843	−	0.743994i
$232$	4.60658			0.302437
$233$	−6.59080	−	11.4156i	−0.431778	−	0.747861i	0.565249	−	0.824920i	$-0.308780\pi$
$233$	−6.59080	−	11.4156i	−0.431778	−	0.747861i	−0.997026	+	0.0770597i	$0.975447\pi$
$234$	−0.196708	+	0.340709i	−0.0128592	+	0.0222728i
$235$	12.1253	−	21.0016i	0.790965	−	1.36999i
$236$	−5.05704	−	8.75905i	−0.329185	−	0.570166i
$237$	−3.70460			−0.240640
$238$	−16.4590	−	7.42036i	−1.06688	−	0.480991i
$239$	4.25442			0.275196			0.137598	−	0.990488i	$-0.456062\pi$
$239$	4.25442			0.275196			0.137598	+	0.990488i	$0.456062\pi$
$240$	1.26426	+	2.18976i	0.0816077	+	0.141349i
$241$	−7.76688	+	13.4526i	−0.500309	+	0.866560i	0.499691	+	0.866204i	$0.333447\pi$
$241$	−7.76688	+	13.4526i	−0.500309	+	0.866560i	−1.00000		0.000356441i	$0.999887\pi$
$242$	−3.72523	+	6.45229i	−0.239467	+	0.414769i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.21317			0.205702
$245$	5.62654	−	16.7815i	0.359466	−	1.07213i
$246$	3.05704			0.194910
$247$	0.393417	+	0.681418i	0.0250325	+	0.0433576i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$	−6.82392	+	11.8194i	−0.432448	+	0.749023i
$250$	4.55966	+	7.89756i	0.288378	+	0.499486i
$251$	−21.4266			−1.35244			−0.676218	−	0.736702i	$-0.736382\pi$
$251$	−21.4266			−1.35244			−0.676218	+	0.736702i	$0.736382\pi$
$252$	−2.41196	−	1.08740i	−0.151939	−	0.0685000i
$253$	−4.29540			−0.270049
$254$	−3.13510	−	5.43016i	−0.196714	−	0.340718i
$255$	8.62721	−	14.9428i	0.540257	−	0.935753i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.76688	−	16.9167i	−0.609241	−	1.05524i	−0.991366	−	0.131126i	$-0.958141\pi$
$257$	−9.76688	−	16.9167i	−0.609241	−	1.05524i	0.382125	−	0.924111i	$-0.375193\pi$
$258$	−2.00000			−0.124515
$259$	2.39342	+	23.8429i	0.148720	+	1.48152i
$260$	0.994763			0.0616926
$261$	−2.30329	−	3.98942i	−0.142570	−	0.246939i
$262$	9.54915	−	16.5396i	0.589948	−	1.02182i
$263$	−8.90198	+	15.4187i	−0.548920	+	0.950757i	0.449429	+	0.893316i	$0.351627\pi$
$263$	−8.90198	+	15.4187i	−0.548920	+	0.950757i	−0.998349	+	0.0574409i	$0.981706\pi$
$264$	2.14770	+	3.71993i	0.132182	+	0.228946i
$265$	0.653150			0.0401227
$266$	−4.29540	+	3.09023i	−0.263368	+	0.189474i
$267$	8.27021			0.506128
$268$	−1.87084	−	3.24040i	−0.114280	−	0.197939i
$269$	9.81603	−	17.0019i	0.598494	−	1.03662i	−0.394550	−	0.918875i	$-0.629099\pi$
$269$	9.81603	−	17.0019i	0.598494	−	1.03662i	0.993044	−	0.117747i	$-0.0375672\pi$
$270$	1.26426	−	2.18976i	0.0769404	−	0.133265i
$271$	−4.68882	−	8.12127i	−0.284825	−	0.493332i	0.687741	−	0.725956i	$-0.258602\pi$
$271$	−4.68882	−	8.12127i	−0.284825	−	0.493332i	−0.972567	+	0.232624i	$0.925269\pi$
$272$	6.82392			0.413761
$273$	−0.844941	+	0.607875i	−0.0511382	+	0.0367903i
$274$	−17.5288			−1.05895
$275$	−2.99264	−	5.18341i	−0.180463	−	0.312571i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	5.96359	−	10.3292i	0.358317	−	0.620624i	−0.629363	−	0.777112i	$-0.716684\pi$
$277$	5.96359	−	10.3292i	0.358317	−	0.620624i	0.987680	+	0.156488i	$0.0500173\pi$
$278$	−6.52063	−	11.2941i	−0.391081	−	0.677373i
$279$	−2.00000			−0.119737
$280$	0.668188	+	6.65638i	0.0399319	+	0.397795i
$281$	−10.6783			−0.637012			−0.318506	−	0.947921i	$-0.603181\pi$
$281$	−10.6783			−0.637012			−0.318506	+	0.947921i	$0.603181\pi$
$282$	−4.79540	−	8.30588i	−0.285562	−	0.494608i
$283$	5.61670	−	9.72841i	0.333878	−	0.578294i	−0.649390	−	0.760455i	$-0.724976\pi$
$283$	5.61670	−	9.72841i	0.333878	−	0.578294i	0.983269	+	0.182161i	$0.0583092\pi$
$284$	6.93050	−	12.0040i	0.411250	−	0.712305i
$285$	−2.52852	−	4.37953i	−0.149777	−	0.259421i
$286$	1.68988			0.0999249
$287$	7.37346	+	3.32424i	0.435242	+	0.196224i
$288$	1.00000			0.0589256
$289$	−14.7829	−	25.6048i	−0.869585	−	1.50617i
$290$	−5.82392	+	10.0873i	−0.341992	+	0.592348i
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	−2.10658	−	3.64871i	−0.123278	−	0.213525i
$293$	22.1764			1.29556			0.647778	−	0.761829i	$-0.275698\pi$
$293$	22.1764			1.29556			0.647778	+	0.761829i	$0.275698\pi$
$294$	−4.63510	−	5.24555i	−0.270325	−	0.305927i
$295$	25.5737			1.48896
$296$	−4.52852	−	7.84363i	−0.263215	−	0.455902i
$297$	2.14770	−	3.71993i	0.124622	−	0.215852i
$298$	0.0311393	−	0.0539349i	0.00180385	−	0.00312436i
$299$	0.196708	+	0.340709i	0.0113759	+	0.0197037i
$300$	−1.39342			−0.0804490
$301$	−4.82392	−	2.17481i	−0.278046	−	0.125354i
$302$	−2.15612			−0.124071
$303$	2.69671	+	4.67084i	0.154922	+	0.268333i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$	−4.06228	+	7.03607i	−0.232605	+	0.402884i
$306$	−3.41196	−	5.90969i	−0.195049	−	0.337834i
$307$	−8.01578			−0.457485			−0.228742	−	0.973487i	$-0.573461\pi$
$307$	−8.01578			−0.457485			−0.228742	+	0.973487i	$0.573461\pi$
$308$	1.13510	+	11.3077i	0.0646785	+	0.644318i
$309$	18.1512			1.03258
$310$	2.52852	+	4.37953i	0.143610	+	0.248740i
$311$	−10.7954	+	18.6982i	−0.612151	+	1.06028i	0.378726	+	0.925509i	$0.376362\pi$
$311$	−10.7954	+	18.6982i	−0.612151	+	1.06028i	−0.990877	+	0.134768i	$0.956971\pi$
$312$	0.196708	−	0.340709i	0.0111364	−	0.0192889i
$313$	−6.59080	−	11.4156i	−0.372534	−	0.645248i	0.617421	−	0.786633i	$-0.288178\pi$
$313$	−6.59080	−	11.4156i	−0.372534	−	0.645248i	−0.989955	+	0.141385i	$0.954844\pi$
$314$	11.0822			0.625407
$315$	5.43050	−	3.90686i	0.305974	−	0.220127i
$316$	3.70460			0.208400
$317$	7.11408	+	12.3220i	0.399567	+	0.692070i	0.993672	−	0.112317i	$-0.0358273\pi$
$317$	7.11408	+	12.3220i	0.399567	+	0.692070i	−0.594106	+	0.804387i	$0.702494\pi$
$318$	0.129157	−	0.223706i	0.00724274	−	0.0125448i
$319$	−9.89356	+	17.1361i	−0.553933	+	0.959440i
$320$	−1.26426	−	2.18976i	−0.0706743	−	0.122411i
$321$	−16.5908			−0.926008
$322$	−2.14770	+	1.54512i	−0.119687	+	0.0861060i
$323$	−13.6478			−0.759386
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.274097	+	0.474750i	−0.0152042	+	0.0263344i
$326$	−6.12721	+	10.6126i	−0.339355	+	0.587780i
$327$	7.28280	+	12.6142i	0.402740	+	0.697566i
$328$	−3.05704			−0.168797
$329$	−2.53447	−	25.2480i	−0.139730	−	1.39197i
$330$	−10.8610			−0.597879
$331$	10.7987	+	18.7039i	0.593552	+	1.02806i	0.993749	+	0.111633i	$0.0356081\pi$
$331$	10.7987	+	18.7039i	0.593552	+	1.02806i	−0.400198	+	0.916429i	$0.631059\pi$
$332$	6.82392	−	11.8194i	0.374511	−	0.648673i
$333$	−4.52852	+	7.84363i	−0.248161	+	0.429828i
$334$	−2.40987	−	4.17403i	−0.131862	−	0.228393i
$335$	9.46093			0.516906
$336$	2.41196	+	1.08740i	0.131583	+	0.0593228i
$337$	13.2132			0.719767			0.359884	−	0.932997i	$-0.382816\pi$
$337$	13.2132			0.719767			0.359884	+	0.932997i	$0.382816\pi$
$338$	6.42261	+	11.1243i	0.349344	+	0.605082i
$339$	−4.55966	+	7.89756i	−0.247647	+	0.428937i
$340$	−8.62721	+	14.9428i	−0.467876	+	0.810385i
$341$	4.29540	+	7.43985i	0.232609	+	0.402890i
$342$	−2.00000			−0.108148
$343$	−5.47565	−	17.6923i	−0.295657	−	0.955294i
$344$	2.00000			0.107833
$345$	−1.26426	−	2.18976i	−0.0680655	−	0.117893i
$346$	−11.4797	+	19.8833i	−0.617150	+	1.06894i
$347$	9.70945	−	16.8173i	0.521230	−	0.902797i	−0.478465	−	0.878107i	$-0.658807\pi$
$347$	9.70945	−	16.8173i	0.521230	−	0.902797i	0.999695	−	0.0246907i	$-0.00786009\pi$
$348$	2.30329	+	3.98942i	0.123469	+	0.213855i
$349$	−5.80262			−0.310607			−0.155303	−	0.987867i	$-0.549636\pi$
$349$	−5.80262			−0.310607			−0.155303	+	0.987867i	$0.549636\pi$
$350$	−3.36087	−	1.51521i	−0.179646	−	0.0809912i
$351$	−0.393417			−0.0209990
$352$	−2.14770	−	3.71993i	−0.114473	−	0.198273i
$353$	−10.4715	+	18.1371i	−0.557341	+	0.965342i	0.440377	+	0.897813i	$0.354845\pi$
$353$	−10.4715	+	18.1371i	−0.557341	+	0.965342i	−0.997717	+	0.0675291i	$0.978488\pi$
$354$	5.05704	−	8.75905i	0.268779	−	0.465538i
$355$	17.5239	+	30.3523i	0.930073	+	1.61093i
$356$	−8.27021			−0.438320
$357$	−1.80329	−	17.9641i	−0.0954403	−	0.950762i
$358$	21.8452			1.15456
$359$	2.35244	+	4.07455i	0.124157	+	0.215046i	0.921403	−	0.388608i	$-0.127044\pi$
$359$	2.35244	+	4.07455i	0.124157	+	0.215046i	−0.797246	+	0.603654i	$0.793711\pi$
$360$	−1.26426	+	2.18976i	−0.0666324	+	0.115411i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	11.0497	+	19.1386i	0.580758	+	1.00590i
$363$	−7.45046			−0.391048
$364$	0.844941	−	0.607875i	0.0442870	−	0.0318613i
$365$	10.6531			0.557608
$366$	1.60658	+	2.78268i	0.0839774	+	0.145453i
$367$	4.71996	−	8.17520i	0.246380	−	0.426742i	−0.716139	−	0.697958i	$-0.754092\pi$
$367$	4.71996	−	8.17520i	0.246380	−	0.426742i	0.962519	+	0.271216i	$0.0874256\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	1.52852	+	2.64748i	0.0795716	+	0.137822i
$370$	22.9009			1.19056
$371$	0.554779	−	0.399124i	0.0288027	−	0.0207215i
$372$	2.00000			0.103695
$373$	−5.83652	−	10.1091i	−0.302203	−	0.523432i	0.674431	−	0.738338i	$-0.264389\pi$
$373$	−5.83652	−	10.1091i	−0.302203	−	0.523432i	−0.976635	+	0.214906i	$0.931056\pi$
$374$	−14.6557	+	25.3845i	−0.757830	+	1.31260i
$375$	−4.55966	+	7.89756i	−0.235460	+	0.407828i
$376$	4.79540	+	8.30588i	0.247304	+	0.428343i
$377$	1.81231			0.0933386
$378$	−0.264260	−	2.63252i	−0.0135921	−	0.135402i
$379$	9.42944			0.484358			0.242179	−	0.970232i	$-0.422138\pi$
$379$	9.42944			0.484358			0.242179	+	0.970232i	$0.422138\pi$
$380$	2.52852	+	4.37953i	0.129710	+	0.224665i
$381$	3.13510	−	5.43016i	0.160616	−	0.278195i
$382$	4.13510	−	7.16221i	0.211570	−	0.366451i
$383$	11.7049	+	20.2735i	0.598092	+	1.03592i	0.993103	+	0.117249i	$0.0374074\pi$
$383$	11.7049	+	20.2735i	0.598092	+	1.03592i	−0.395011	+	0.918676i	$0.629259\pi$
$384$	−1.00000			−0.0510310
$385$	−26.1963	−	11.8103i	−1.33509	−	0.601909i
$386$	−6.50750			−0.331223
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	11.0371	−	19.1168i	0.559603	−	0.969260i	−0.437927	−	0.899011i	$-0.644287\pi$
$389$	11.0371	−	19.1168i	0.559603	−	0.969260i	0.997529	−	0.0702494i	$-0.0223795\pi$
$390$	0.497381	+	0.861490i	0.0251859	+	0.0436232i
$391$	−6.82392			−0.345100
$392$	4.63510	+	5.24555i	0.234108	+	0.264940i
$393$	19.0983			0.963382
$394$	−4.09013	−	7.08430i	−0.206058	−	0.356902i
$395$	−4.68358	+	8.11220i	−0.235656	+	0.408169i
$396$	−2.14770	+	3.71993i	−0.107926	+	0.186933i
$397$	8.41405	+	14.5736i	0.422289	+	0.731426i	0.996163	−	0.0875178i	$-0.0278935\pi$
$397$	8.41405	+	14.5736i	0.422289	+	0.731426i	−0.573874	+	0.818944i	$0.694560\pi$
$398$	−14.4095			−0.722282
$399$	−4.82392	−	2.17481i	−0.241498	−	0.108877i
$400$	1.39342			0.0696708
$401$	−3.11656	−	5.39804i	−0.155634	−	0.269565i	0.777656	−	0.628690i	$-0.216409\pi$
$401$	−3.11656	−	5.39804i	−0.155634	−	0.269565i	−0.933290	+	0.359125i	$0.883075\pi$
$402$	1.87084	−	3.24040i	0.0933092	−	0.161616i
$403$	0.393417	−	0.681418i	0.0195975	−	0.0339439i
$404$	−2.69671	−	4.67084i	−0.134166	−	0.232383i
$405$	2.52852			0.125643
$406$	1.21734	+	12.1269i	0.0604154	+	0.601849i
$407$	38.9036			1.92838
$408$	3.41196	+	5.90969i	0.168917	+	0.292573i
$409$	−0.184646	+	0.319815i	−0.00913013	+	0.0158139i	−0.870554	−	0.492072i	$-0.836240\pi$
$409$	−0.184646	+	0.319815i	−0.00913013	+	0.0158139i	0.861424	+	0.507886i	$0.169573\pi$
$410$	3.86490	−	6.69420i	0.190874	−	0.330603i
$411$	−8.76440	−	15.1804i	−0.432316	−	0.748793i
$412$	−18.1512			−0.894244
$413$	21.7220	−	15.6274i	1.06887	−	0.768976i
$414$	−1.00000			−0.0491473
$415$	17.2544	+	29.8855i	0.846986	+	1.46702i
$416$	−0.196708	+	0.340709i	−0.00964443	+	0.0167046i
$417$	6.52063	−	11.2941i	0.319317	−	0.553073i
$418$	4.29540	+	7.43985i	0.210095	+	0.363895i
$419$	30.4837			1.48922			0.744612	−	0.667498i	$-0.232635\pi$
$419$	30.4837			1.48922			0.744612	+	0.667498i	$0.232635\pi$
$420$	−5.43050	+	3.90686i	−0.264981	+	0.190635i
$421$	34.2954			1.67146			0.835728	−	0.549144i	$-0.185046\pi$
$421$	34.2954			1.67146			0.835728	+	0.549144i	$0.185046\pi$
$422$	−7.59869	−	13.1613i	−0.369899	−	0.640683i
$423$	4.79540	−	8.30588i	0.233160	−	0.403846i
$424$	−0.129157	+	0.223706i	−0.00627240	+	0.0108641i
$425$	−4.75428	−	8.23466i	−0.230617	−	0.399440i
$426$	13.8610			0.671568
$427$	0.849112	+	8.45873i	0.0410914	+	0.409347i
$428$	16.5908			0.801947
$429$	0.844941	+	1.46348i	0.0407942	+	0.0706575i
$430$	−2.52852	+	4.37953i	−0.121936	+	0.211200i
$431$	−16.0983	+	27.8831i	−0.775428	+	1.34308i	0.159126	+	0.987258i	$0.449132\pi$
$431$	−16.0983	+	27.8831i	−0.775428	+	1.34308i	−0.934554	+	0.355822i	$0.884201\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−22.5592			−1.08413			−0.542064	−	0.840337i	$-0.682357\pi$
$433$	−22.5592			−1.08413			−0.542064	+	0.840337i	$0.682357\pi$
$434$	4.82392	+	2.17481i	0.231556	+	0.104394i
$435$	−11.6478			−0.558471
$436$	−7.28280	−	12.6142i	−0.348783	−	0.604110i
$437$	−1.00000	+	1.73205i	−0.0478365	+	0.0828552i
$438$	2.10658	−	3.64871i	0.100656	−	0.174342i
$439$	−2.97481	−	5.15252i	−0.141980	−	0.245916i	0.786262	−	0.617893i	$-0.212013\pi$
$439$	−2.97481	−	5.15252i	−0.141980	−	0.245916i	−0.928242	+	0.371977i	$0.878680\pi$
$440$	10.8610			0.517778
$441$	2.22523	−	6.63689i	0.105963	−	0.316043i
$442$	2.68465			0.127696
$443$	−7.62197	−	13.2016i	−0.362131	−	0.627229i	0.626180	−	0.779678i	$-0.284617\pi$
$443$	−7.62197	−	13.2016i	−0.362131	−	0.627229i	−0.988311	+	0.152449i	$0.951284\pi$
$444$	4.52852	−	7.84363i	0.214914	−	0.372242i
$445$	10.4557	−	18.1098i	0.495648	−	0.858487i
$446$	10.5856	+	18.3347i	0.501241	+	0.868175i
$447$	0.0622786			0.00294568
$448$	−2.41196	−	1.08740i	−0.113954	−	0.0513750i
$449$	−22.5488			−1.06414			−0.532071	−	0.846700i	$-0.678586\pi$
$449$	−22.5488			−1.06414			−0.532071	+	0.846700i	$0.678586\pi$
$450$	−0.696708	−	1.20673i	−0.0328432	−	0.0568860i
$451$	6.56561	−	11.3720i	0.309162	−	0.535485i
$452$	4.55966	−	7.89756i	0.214468	−	0.371470i
$453$	−1.07806	−	1.86726i	−0.0506518	−	0.0877315i
$454$	−2.40948			−0.113083
$455$	0.262876	+	2.61873i	0.0123238	+	0.122768i
$456$	2.00000			0.0936586
$457$	−1.05704	−	1.83085i	−0.0494463	−	0.0856435i	0.840243	−	0.542210i	$-0.182412\pi$
$457$	−1.05704	−	1.83085i	−0.0494463	−	0.0856435i	−0.889689	+	0.456567i	$0.849079\pi$
$458$	−5.30800	+	9.19372i	−0.248026	+	0.429594i
$459$	3.41196	−	5.90969i	0.159257	−	0.275841i
$460$	1.26426	+	2.18976i	0.0589464	+	0.102098i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−9.22523	+	6.63689i	−0.429197	+	0.308776i
$463$	−2.42633			−0.112761			−0.0563806	−	0.998409i	$-0.517956\pi$
$463$	−2.42633			−0.112761			−0.0563806	+	0.998409i	$0.517956\pi$
$464$	−2.30329	−	3.98942i	−0.106928	−	0.185204i
$465$	−2.52852	+	4.37953i	−0.117257	+	0.203096i
$466$	−6.59080	+	11.4156i	−0.305313	+	0.528817i
$467$	9.89356	+	17.1361i	0.457819	+	0.792966i	0.998845	−	0.0480395i	$-0.0152973\pi$
$467$	9.89356	+	17.1361i	0.457819	+	0.792966i	−0.541026	+	0.841006i	$0.681964\pi$
$468$	0.393417			0.0181857
$469$	8.03602	−	5.78134i	0.371069	−	0.266958i
$470$	−24.2505			−1.11859
$471$	5.54112	+	9.59750i	0.255321	+	0.442229i
$472$	−5.05704	+	8.75905i	−0.232769	+	0.403168i
$473$	−4.29540	+	7.43985i	−0.197503	+	0.342085i
$474$	1.85230	+	3.20828i	0.0850790	+	0.147361i
$475$	−2.78683			−0.127869
$476$	1.80329	+	17.9641i	0.0826537	+	0.823384i
$477$	0.258313			0.0118273
$478$	−2.12721	−	3.68444i	−0.0972964	−	0.168522i
$479$	−11.0623	+	19.1604i	−0.505448	+	0.875462i	0.494532	+	0.869160i	$0.335340\pi$
$479$	−11.0623	+	19.1604i	−0.505448	+	0.875462i	−0.999980	+	0.00630275i	$0.997994\pi$
$480$	1.26426	−	2.18976i	0.0577053	−	0.0999486i
$481$	−1.78160	−	3.08582i	−0.0812338	−	0.140701i
$482$	15.5338			0.707543
$483$	−2.41196	−	1.08740i	−0.109748	−	0.0494786i
$484$	7.45046			0.338657
$485$	10.1141	+	17.5181i	0.459257	+	0.795456i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−4.27438	+	7.40344i	−0.193691	+	0.335482i	−0.946470	−	0.322790i	$-0.895379\pi$
$487$	−4.27438	+	7.40344i	−0.193691	+	0.335482i	0.752780	+	0.658272i	$0.228712\pi$
$488$	−1.60658	−	2.78268i	−0.0727266	−	0.125966i
$489$	−12.2544			−0.554164
$490$	−17.3465	+	3.51804i	−0.783635	+	0.158929i
$491$	22.4360			1.01252			0.506262	−	0.862380i	$-0.331027\pi$
$491$	22.4360			1.01252			0.506262	+	0.862380i	$0.331027\pi$
$492$	−1.52852	−	2.64748i	−0.0689110	−	0.119357i
$493$	−15.7175	+	27.2235i	−0.707880	+	1.22608i
$494$	0.393417	−	0.681418i	0.0177007	−	0.0306584i
$495$	−5.43050	−	9.40591i	−0.244083	−	0.422764i
$496$	−2.00000			−0.0898027
$497$	33.4322	+	15.0725i	1.49964	+	0.676095i
$498$	13.6478			0.611574
$499$	18.2465	+	31.6039i	0.816827	+	1.41479i	0.908009	+	0.418952i	$0.137602\pi$
$499$	18.2465	+	31.6039i	0.816827	+	1.41479i	−0.0911817	+	0.995834i	$0.529064\pi$
$500$	4.55966	−	7.89756i	0.203914	−	0.353190i
$501$	2.40987	−	4.17403i	0.107665	−	0.186482i
$502$	10.7133	+	18.5560i	0.478158	+	0.828194i
$503$	38.4585			1.71478			0.857389	−	0.514669i	$-0.172085\pi$
$503$	38.4585			1.71478			0.857389	+	0.514669i	$0.172085\pi$
$504$	0.264260	+	2.63252i	0.0117711	+	0.117262i
$505$	13.6374			0.606855
$506$	2.14770	+	3.71993i	0.0954769	+	0.165371i
$507$	−6.42261	+	11.1243i	−0.285238	+	0.494047i
$508$	−3.13510	+	5.43016i	−0.139098	+	0.240924i
$509$	−11.2875	−	19.5505i	−0.500310	−	0.866562i	−1.00000		0.000357978i	$-0.999886\pi$
$509$	−11.2875	−	19.5505i	−0.500310	−	0.866562i	0.499690	−	0.866204i	$-0.333447\pi$
$510$	−17.2544			−0.764039
$511$	9.04862	−	6.50983i	0.400287	−	0.287978i
$512$	1.00000			0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	−9.76688	+	16.9167i	−0.430799	+	0.746165i
$515$	22.9478	−	39.7468i	1.01120	−	1.75145i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−41.1963			−1.81181
$518$	19.4518	−	13.9942i	0.854663	−	0.614869i
$519$	−22.9593			−1.00780
$520$	−0.497381	−	0.861490i	−0.0218116	−	0.0377788i
$521$	−8.76759	+	15.1859i	−0.384115	+	0.665307i	−0.991646	−	0.128989i	$-0.958827\pi$
$521$	−8.76759	+	15.1859i	−0.384115	+	0.665307i	0.607531	+	0.794296i	$0.292160\pi$
$522$	−2.30329	+	3.98942i	−0.100812	+	0.174612i
$523$	−10.1505	−	17.5811i	−0.443849	−	0.768768i	0.554123	−	0.832435i	$-0.313054\pi$
$523$	−10.1505	−	17.5811i	−0.443849	−	0.768768i	−0.997971	+	0.0636667i	$0.979721\pi$
$524$	−19.0983			−0.834313
$525$	−0.368225	−	3.66820i	−0.0160706	−	0.160093i
$526$	17.8040			0.776290
$527$	6.82392	+	11.8194i	0.297255	+	0.514860i
$528$	2.14770	−	3.71993i	0.0934666	−	0.161889i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−0.326575	−	0.565644i	−0.0141855	−	0.0245700i
$531$	10.1141			0.438914
$532$	4.82392	+	2.17481i	0.209143	+	0.0942899i
$533$	−1.20269			−0.0520944
$534$	−4.13510	−	7.16221i	−0.178943	−	0.309939i
$535$	−20.9751	+	36.3299i	−0.906832	+	1.57068i
$536$	−1.87084	+	3.24040i	−0.0808081	+	0.139964i
$537$	10.9226	+	18.9185i	0.471345	+	0.816394i
$538$	−19.6321			−0.846398
$539$	−29.4679	+	5.97637i	−1.26927	+	0.257420i
$540$	−2.52852			−0.108810
$541$	−15.9016	−	27.5424i	−0.683663	−	1.18414i	−0.973855	−	0.227170i	$-0.927053\pi$
$541$	−15.9016	−	27.5424i	−0.683663	−	1.18414i	0.290192	−	0.956968i	$-0.406281\pi$
$542$	−4.68882	+	8.12127i	−0.201402	+	0.348838i
$543$	−11.0497	+	19.1386i	−0.474187	+	0.821316i
$544$	−3.41196	−	5.90969i	−0.146287	−	0.253376i
$545$	36.8294			1.57760
$546$	0.948906	+	0.427803i	0.0406094	+	0.0183083i
$547$	29.5817			1.26482			0.632410	−	0.774633i	$-0.282066\pi$
$547$	29.5817			1.26482			0.632410	+	0.774633i	$0.282066\pi$
$548$	8.76440	+	15.1804i	0.374397	+	0.648474i
$549$	−1.60658	+	2.78268i	−0.0685673	+	0.118762i
$550$	−2.99264	+	5.18341i	−0.127607	+	0.221021i
$551$	4.60658	+	7.97884i	0.196247	+	0.339910i
$552$	1.00000			0.0425628
$553$	0.978979	+	9.75244i	0.0416304	+	0.414716i
$554$	−11.9272			−0.506737
$555$	11.4505	+	19.8328i	0.486045	+	0.841854i
$556$	−6.52063	+	11.2941i	−0.276536	+	0.478975i
$557$	10.7511	−	18.6214i	0.455539	−	0.789016i	−0.543180	−	0.839616i	$-0.682780\pi$
$557$	10.7511	−	18.6214i	0.455539	−	0.789016i	0.998719	+	0.0506001i	$0.0161134\pi$
$558$	1.00000	+	1.73205i	0.0423334	+	0.0733236i
$559$	0.786834			0.0332795
$560$	5.43050	−	3.90686i	0.229481	−	0.165095i
$561$	−29.3115			−1.23753
$562$	5.33914	+	9.24765i	0.225218	+	0.390089i
$563$	15.7333	−	27.2508i	0.663078	−	1.14848i	−0.316725	−	0.948518i	$-0.602583\pi$
$563$	15.7333	−	27.2508i	0.663078	−	1.14848i	0.979803	−	0.199967i	$-0.0640835\pi$
$564$	−4.79540	+	8.30588i	−0.201923	+	0.349740i
$565$	11.5292	+	19.9692i	0.485037	+	0.840108i
$566$	−11.2334			−0.472175
$567$	2.14770	−	1.54512i	0.0901949	−	0.0648888i
$568$	−13.8610			−0.581595
$569$	18.7360	+	32.4517i	0.785455	+	1.36045i	0.928727	+	0.370764i	$0.120904\pi$
$569$	18.7360	+	32.4517i	0.785455	+	1.36045i	−0.143272	+	0.989683i	$0.545762\pi$
$570$	−2.52852	+	4.37953i	−0.105908	+	0.183438i
$571$	−14.1042	+	24.4293i	−0.590244	+	1.02233i	0.403955	+	0.914779i	$0.367635\pi$
$571$	−14.1042	+	24.4293i	−0.590244	+	1.02233i	−0.994199	+	0.107554i	$0.965698\pi$
$572$	−0.844941	−	1.46348i	−0.0353288	−	0.0611912i
$573$	8.27021			0.345493
$574$	−0.807855	−	8.04773i	−0.0337192	−	0.335906i
$575$	−1.39342			−0.0581095
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.43840	+	2.49137i	−0.0598812	+	0.103717i	−0.894412	−	0.447244i	$-0.852406\pi$
$577$	−1.43840	+	2.49137i	−0.0598812	+	0.103717i	0.834531	+	0.550961i	$0.185739\pi$
$578$	−14.7829	+	25.6048i	−0.614889	+	1.06502i
$579$	−3.25375	−	5.63566i	−0.135221	−	0.234210i
$580$	11.6478			0.483650
$581$	32.9180	+	14.8407i	1.36567	+	0.615697i
$582$	8.00000			0.331611
$583$	−0.554779	−	0.960905i	−0.0229766	−	0.0397966i
$584$	−2.10658	+	3.64871i	−0.0871710	+	0.150985i
$585$	−0.497381	+	0.861490i	−0.0205642	+	0.0356182i
$586$	−11.0882	−	19.2053i	−0.458049	−	0.793363i
$587$	−19.8873			−0.820835			−0.410418	−	0.911898i	$-0.634617\pi$
$587$	−19.8873			−0.820835			−0.410418	+	0.911898i	$0.634617\pi$
$588$	−2.22523	+	6.63689i	−0.0917669	+	0.273701i
$589$	4.00000			0.164817
$590$	−12.7868	−	22.1474i	−0.526426	−	0.911796i
$591$	4.09013	−	7.08430i	0.168245	−	0.291409i
$592$	−4.52852	+	7.84363i	−0.186121	+	0.322371i
$593$	0.553713	+	0.959059i	0.0227383	+	0.0393838i	0.877171	−	0.480179i	$-0.159428\pi$
$593$	0.553713	+	0.959059i	0.0227383	+	0.0393838i	−0.854432	+	0.519563i	$0.826095\pi$
$594$	−4.29540			−0.176242
$595$	−41.6170	−	18.7625i	−1.70613	−	0.769189i
$596$	−0.0622786			−0.00255103
$597$	−7.20474	−	12.4790i	−0.294870	−	0.510731i
$598$	0.196708	−	0.340709i	0.00804401	−	0.0139326i
$599$	14.8735	−	25.7616i	0.607713	−	1.05259i	−0.383903	−	0.923373i	$-0.625420\pi$
$599$	14.8735	−	25.7616i	0.607713	−	1.05259i	0.991616	−	0.129217i	$-0.0412463\pi$
$600$	0.696708	+	1.20673i	0.0284430	+	0.0492647i
$601$	−3.88592			−0.158510			−0.0792549	−	0.996854i	$-0.525254\pi$
$601$	−3.88592			−0.158510			−0.0792549	+	0.996854i	$0.525254\pi$
$602$	0.528521	+	5.26504i	0.0215409	+	0.214587i
$603$	3.74169			0.152373
$604$	1.07806	+	1.86726i	0.0438657	+	0.0759777i
$605$	−9.41932	+	16.3147i	−0.382950	+	0.663288i
$606$	2.69671	−	4.67084i	0.109546	−	0.189740i
$607$	0.978979	+	1.69564i	0.0397355	+	0.0688240i	0.885209	−	0.465193i	$-0.154015\pi$
$607$	0.978979	+	1.69564i	0.0397355	+	0.0688240i	−0.845474	+	0.534017i	$0.820682\pi$
$608$	−2.00000			−0.0811107
$609$	−9.89356	+	7.11771i	−0.400907	+	0.288424i
$610$	8.12456			0.328954
$611$	1.88659	+	3.26767i	0.0763233	+	0.132196i
$612$	−3.41196	+	5.90969i	−0.137920	+	0.238885i
$613$	1.97162	−	3.41495i	0.0796330	−	0.137928i	−0.823459	−	0.567376i	$-0.807958\pi$
$613$	1.97162	−	3.41495i	0.0796330	−	0.137928i	0.903092	+	0.429448i	$0.141292\pi$
$614$	4.00789	+	6.94187i	0.161745	+	0.280151i
$615$	7.72979			0.311695
$616$	9.22523	−	6.63689i	0.371695	−	0.267408i
$617$	−20.8876			−0.840904			−0.420452	−	0.907315i	$-0.638128\pi$
$617$	−20.8876			−0.840904			−0.420452	+	0.907315i	$0.638128\pi$
$618$	−9.07558	−	15.7194i	−0.365074	−	0.632326i
$619$	−14.6009	+	25.2895i	−0.586860	+	1.01647i	0.407780	+	0.913080i	$0.366303\pi$
$619$	−14.6009	+	25.2895i	−0.586860	+	1.01647i	−0.994641	+	0.103392i	$0.967030\pi$
$620$	2.52852	−	4.37953i	0.101548	−	0.175886i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	21.5908			0.865712
$623$	−2.18549	−	21.7715i	−0.0875597	−	0.872257i
$624$	−0.393417			−0.0157493
$625$	15.0127	+	26.0028i	0.600509	+	1.04011i
$626$	−6.59080	+	11.4156i	−0.263421	+	0.456259i
$627$	−4.29540	+	7.43985i	−0.171542	+	0.297119i
$628$	−5.54112	−	9.59750i	−0.221115	−	0.382982i
$629$	61.8045			2.46431
$630$	−6.09869	−	2.74952i	−0.242978	−	0.109544i
$631$	−16.2653			−0.647509			−0.323755	−	0.946141i	$-0.604945\pi$
$631$	−16.2653			−0.647509			−0.323755	+	0.946141i	$0.604945\pi$
$632$	−1.85230	−	3.20828i	−0.0736805	−	0.127618i
$633$	7.59869	−	13.1613i	0.302021	−	0.523115i
$634$	7.11408	−	12.3220i	0.282536	−	0.489367i
$635$	−7.92717	−	13.7303i	−0.314580	−	0.544869i
$636$	−0.258313			−0.0102428
$637$	1.82353	+	2.06369i	0.0722508	+	0.0817663i
$638$	19.7871			0.783379
$639$	6.93050	+	12.0040i	0.274166	+	0.474870i
$640$	−1.26426	+	2.18976i	−0.0499743	+	0.0865580i
$641$	12.3087	−	21.3193i	0.486165	−	0.842062i	−0.513709	−	0.857965i	$-0.671729\pi$
$641$	12.3087	−	21.3193i	0.486165	−	0.842062i	0.999874	+	0.0159027i	$0.00506219\pi$
$642$	8.29540	+	14.3681i	0.327393	+	0.567062i
$643$	−15.2132			−0.599949			−0.299974	−	0.953947i	$-0.596978\pi$
$643$	−15.2132			−0.599949			−0.299974	+	0.953947i	$0.596978\pi$
$644$	2.41196	+	1.08740i	0.0950445	+	0.0428497i
$645$	−5.05704			−0.199121
$646$	6.82392	+	11.8194i	0.268484	+	0.465027i
$647$	−5.53641	+	9.58935i	−0.217659	+	0.376996i	−0.954092	−	0.299514i	$-0.903175\pi$
$647$	−5.53641	+	9.58935i	−0.217659	+	0.376996i	0.736433	+	0.676511i	$0.236509\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−21.7220	−	37.6236i	−0.852664	−	1.47686i
$650$	0.548194			0.0215019
$651$	0.528521	+	5.26504i	0.0207144	+	0.206353i
$652$	12.2544			0.479920
$653$	−20.0292	−	34.6916i	−0.783803	−	1.35759i	−0.929712	−	0.368288i	$-0.879944\pi$
$653$	−20.0292	−	34.6916i	−0.783803	−	1.35759i	0.145909	−	0.989298i	$-0.453389\pi$
$654$	7.28280	−	12.6142i	0.284780	−	0.493254i
$655$	24.1452	−	41.8208i	0.943432	−	1.63407i
$656$	1.52852	+	2.64748i	0.0596787	+	0.103367i
$657$	4.21317			0.164371
$658$	−20.5982	+	14.8189i	−0.803000	+	0.577701i
$659$	−42.3380			−1.64925			−0.824627	−	0.565676i	$-0.808615\pi$
$659$	−42.3380			−1.64925			−0.824627	+	0.565676i	$0.808615\pi$
$660$	5.43050	+	9.40591i	0.211382	+	0.366124i
$661$	7.74905	−	13.4217i	0.301403	−	0.522045i	−0.675051	−	0.737771i	$-0.735878\pi$
$661$	7.74905	−	13.4217i	0.301403	−	0.522045i	0.976454	+	0.215726i	$0.0692117\pi$
$662$	10.7987	−	18.7039i	0.419704	−	0.726950i
$663$	1.34232	+	2.32497i	0.0521315	+	0.0902944i
$664$	−13.6478			−0.529639
$665$	−10.8610	+	7.81372i	−0.421172	+	0.303003i
$666$	9.05704			0.350953
$667$	2.30329	+	3.98942i	0.0891838	+	0.154471i
$668$	−2.40987	+	4.17403i	−0.0932409	+	0.161498i
$669$	−10.5856	+	18.3347i	−0.409261	+	0.708862i
$670$	−4.73047	−	8.19341i	−0.182754	−	0.316539i
$671$	13.8018			0.532814
$672$	−0.264260	−	2.63252i	−0.0101941	−	0.101552i
$673$	−37.1875			−1.43347			−0.716736	−	0.697345i	$-0.754365\pi$
$673$	−37.1875			−1.43347			−0.716736	+	0.697345i	$0.754365\pi$
$674$	−6.60658	−	11.4429i	−0.254476	−	0.440765i
$675$	0.696708	−	1.20673i	0.0268163	−	0.0464472i
$676$	6.42261	−	11.1243i	0.247024	−	0.427857i
$677$	12.3584	+	21.4054i	0.474971	+	0.822675i	0.999589	−	0.0286633i	$-0.00912505\pi$
$677$	12.3584	+	21.4054i	0.474971	+	0.822675i	−0.524618	+	0.851338i	$0.675792\pi$
$678$	9.11932			0.350225
$679$	19.2957	+	8.69923i	0.740500	+	0.333846i
$680$	17.2544			0.661677
$681$	−1.20474	−	2.08667i	−0.0461658	−	0.0799615i
$682$	4.29540	−	7.43985i	0.164479	−	0.284887i
$683$	21.0325	−	36.4294i	0.804787	−	1.39393i	−0.111648	−	0.993748i	$-0.535613\pi$
$683$	21.0325	−	36.4294i	0.804787	−	1.39393i	0.916435	−	0.400184i	$-0.131054\pi$
$684$	1.00000	+	1.73205i	0.0382360	+	0.0662266i
$685$	−44.3219			−1.69345
$686$	−12.5842	+	13.5882i	−0.480465	+	0.518800i
$687$	−10.6160			−0.405025
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−0.0508124	+	0.0880096i	−0.00193580	+	0.00335290i
$690$	−1.26426	+	2.18976i	−0.0481296	+	0.0833629i
$691$	5.26232	+	9.11460i	0.200188	+	0.346736i	0.948589	−	0.316511i	$-0.102511\pi$
$691$	5.26232	+	9.11460i	0.200188	+	0.346736i	−0.748401	+	0.663247i	$0.769178\pi$
$692$	22.9593			0.872782
$693$	−10.3603	−	4.67084i	−0.393557	−	0.177430i
$694$	−19.4189			−0.737131
$695$	−16.4875	−	28.5573i	−0.625408	−	1.08324i
$696$	2.30329	−	3.98942i	0.0873060	−	0.151218i
$697$	10.4305	−	18.0662i	0.395083	−	0.684305i
$698$	2.90131	+	5.02521i	0.109816	+	0.190207i
$699$	−13.1816			−0.498574
$700$	0.368225	+	3.66820i	0.0139176	+	0.138645i
$701$	−28.1764			−1.06421			−0.532103	−	0.846679i	$-0.678598\pi$
$701$	−28.1764			−1.06421			−0.532103	+	0.846679i	$0.678598\pi$
$702$	0.196708	+	0.340709i	0.00742428	+	0.0128592i
$703$	9.05704	−	15.6873i	0.341593	−	0.591656i
$704$	−2.14770	+	3.71993i	−0.0809445	+	0.140200i
$705$	−12.1253	−	21.0016i	−0.456664	−	0.790965i
$706$	20.9430			0.788199
$707$	11.5834	−	8.33346i	0.435640	−	0.313412i
$708$	−10.1141			−0.380111
$709$	1.93036	+	3.34349i	0.0724963	+	0.125567i	0.899995	−	0.435901i	$-0.143570\pi$
$709$	1.93036	+	3.34349i	0.0724963	+	0.125567i	−0.827498	+	0.561468i	$0.810237\pi$
$710$	17.5239	−	30.3523i	0.657661	−	1.13910i
$711$	−1.85230	+	3.20828i	−0.0694667	+	0.120320i
$712$	4.13510	+	7.16221i	0.154970	+	0.268415i
$713$	2.00000			0.0749006
$714$	−14.6557	+	10.5438i	−0.548477	+	0.394590i
$715$	4.27290			0.159798
$716$	−10.9226	−	18.9185i	−0.408197	−	0.707018i
$717$	2.12721	−	3.68444i	0.0794422	−	0.137598i
$718$	2.35244	−	4.07455i	0.0877923	−	0.152061i
$719$	15.2590	+	26.4293i	0.569064	+	0.985648i	0.996659	+	0.0816775i	$0.0260277\pi$
$719$	15.2590	+	26.4293i	0.569064	+	0.985648i	−0.427595	+	0.903971i	$0.640639\pi$
$720$	2.52852			0.0942324
$721$	−4.79663	−	47.7833i	−0.178636	−	1.77954i
$722$	−15.0000			−0.558242
$723$	7.76688	+	13.4526i	0.288853	+	0.500309i
$724$	11.0497	−	19.1386i	0.410658	−	0.711281i
$725$	−3.20945	+	5.55892i	−0.119196	+	0.206453i
$726$	3.72523	+	6.45229i	0.138256	+	0.239467i
$727$	−14.3591			−0.532549			−0.266275	−	0.963897i	$-0.585793\pi$
$727$	−14.3591			−0.532549			−0.266275	+	0.963897i	$0.585793\pi$
$728$	−0.948906	−	0.427803i	−0.0351688	−	0.0158554i
$729$	1.00000			0.0370370
$730$	−5.32654	−	9.22584i	−0.197144	−	0.341464i
$731$	−6.82392	+	11.8194i	−0.252392	+	0.437155i
$732$	1.60658	−	2.78268i	0.0593810	−	0.102851i
$733$	5.95555	+	10.3153i	0.219973	+	0.381005i	0.954800	−	0.297250i	$-0.0960696\pi$
$733$	5.95555	+	10.3153i	0.219973	+	0.381005i	−0.734826	+	0.678256i	$0.762736\pi$
$734$	−9.43991			−0.348434
$735$	−11.7200	−	13.2635i	−0.432297	−	0.489231i
$736$	−1.00000			−0.0368605
$737$	−8.03602	−	13.9188i	−0.296011	−	0.512705i
$738$	1.52852	−	2.64748i	0.0562656	−	0.0974549i
$739$	20.5619	−	35.6142i	0.756381	−	1.31009i	−0.188304	−	0.982111i	$-0.560299\pi$
$739$	20.5619	−	35.6142i	0.756381	−	1.31009i	0.944685	−	0.327980i	$-0.106368\pi$
$740$	−11.4505	−	19.8328i	−0.420927	−	0.729067i
$741$	0.786834			0.0289051
$742$	−0.623041	−	0.280891i	−0.0228726	−	0.0103118i
$743$	10.8610			0.398452			0.199226	−	0.979954i	$-0.436157\pi$
$743$	10.8610			0.398452			0.199226	+	0.979954i	$0.436157\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$	0.0787364	−	0.136375i	0.00288468	−	0.00499641i
$746$	−5.83652	+	10.1091i	−0.213690	+	0.370122i
$747$	6.82392	+	11.8194i	0.249674	+	0.432448i
$748$	29.3115			1.07173
$749$	4.38429	+	43.6756i	0.160198	+	1.59587i
$750$	9.11932			0.332990
$751$	26.3367	+	45.6164i	0.961038	+	1.66457i	0.719902	+	0.694076i	$0.244187\pi$
$751$	26.3367	+	45.6164i	0.961038	+	1.66457i	0.241136	+	0.970491i	$0.422480\pi$
$752$	4.79540	−	8.30588i	0.174870	−	0.302884i
$753$	−10.7133	+	18.5560i	−0.390415	+	0.676218i
$754$	−0.906154	−	1.56950i	−0.0330002	−	0.0571580i
$755$	−5.45181			−0.198412
$756$	−2.14770	+	1.54512i	−0.0781111	+	0.0561953i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	−4.71472	−	8.16613i	−0.171246	−	0.296607i
$759$	−2.14770	+	3.71993i	−0.0779566	+	0.135025i
$760$	2.52852	−	4.37953i	0.0917191	−	0.158862i
$761$	−3.68882	−	6.38922i	−0.133719	−	0.231609i	0.791388	−	0.611314i	$-0.209359\pi$
$761$	−3.68882	−	6.38922i	−0.133719	−	0.231609i	−0.925108	+	0.379705i	$0.876025\pi$
$762$	−6.27021			−0.227146
$763$	31.2826	−	22.5056i	1.13250	−	0.814756i
$764$	−8.27021			−0.299206
$765$	−8.62721	−	14.9428i	−0.311918	−	0.540257i
$766$	11.7049	−	20.2735i	0.422915	−	0.732510i
$767$	−1.98953	+	3.44596i	−0.0718376	+	0.124426i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−26.1462			−0.942857			−0.471428	−	0.881904i	$-0.656261\pi$
$769$	−26.1462			−0.942857			−0.471428	+	0.881904i	$0.656261\pi$
$770$	2.87013	+	28.5918i	0.103432	+	1.03038i
$771$	−19.5338			−0.703491
$772$	3.25375	+	5.63566i	0.117105	+	0.202832i
$773$	−11.3794	+	19.7097i	−0.409289	+	0.708909i	−0.994810	−	0.101748i	$-0.967557\pi$
$773$	−11.3794	+	19.7097i	−0.409289	+	0.708909i	0.585521	+	0.810657i	$0.300890\pi$
$774$	−1.00000	+	1.73205i	−0.0359443	+	0.0622573i
$775$	1.39342	+	2.41347i	0.0500530	+	0.0866944i
$776$	−8.00000			−0.287183
$777$	21.8452	+	9.84867i	0.783693	+	0.353319i
$778$	−22.0742			−0.791397
$779$	−3.05704	−	5.29495i	−0.109530	−	0.189711i
$780$	0.497381	−	0.861490i	0.0178091	−	0.0308463i
$781$	29.7693	−	51.5619i	1.06523	−	1.84503i
$782$	3.41196	+	5.90969i	0.122011	+	0.211330i
$783$	−4.60658			−0.164626
$784$	2.22523	−	6.63689i	0.0794725	−	0.237032i
$785$	28.0217			1.00014
$786$	−9.54915	−	16.5396i	−0.340607	−	0.589948i
$787$	2.79802	−	4.84631i	0.0997386	−	0.172752i	−0.811838	−	0.583883i	$-0.801533\pi$
$787$	2.79802	−	4.84631i	0.0997386	−	0.172752i	0.911576	+	0.411131i	$0.134866\pi$
$788$	−4.09013	+	7.08430i	−0.145705	+	0.252368i
$789$	8.90198	+	15.4187i	0.316919	+	0.548920i
$790$	9.36716			0.333269
$791$	21.9954	+	9.91639i	0.782068	+	0.352586i
$792$	4.29540			0.152630
$793$	−0.632057	−	1.09475i	−0.0224450	−	0.0388759i
$794$	8.41405	−	14.5736i	0.298603	−	0.517196i
$795$	0.326575	−	0.565644i	0.0115824	−	0.0200613i
$796$	7.20474	+	12.4790i	0.255365	+	0.442306i
$797$	52.7993			1.87025			0.935123	−	0.354322i	$-0.115288\pi$
$797$	52.7993			1.87025			0.935123	+	0.354322i	$0.115288\pi$
$798$	0.528521	+	5.26504i	0.0187094	+	0.186380i
$799$	−65.4469			−2.31534
$800$	−0.696708	−	1.20673i	−0.0246324	−	0.0426645i
$801$	4.13510	−	7.16221i	0.146107	−	0.253064i
$802$	−3.11656	+	5.39804i	−0.110050	+	0.190611i
$803$	−9.04862	−	15.6727i	−0.319319	−	0.553076i
$804$	−3.74169			−0.131959
$805$	−5.43050	+	3.90686i	−0.191400	+	0.137699i
$806$	−0.786834			−0.0277150
$807$	−9.81603	−	17.0019i	−0.345541	−	0.598494i
$808$	−2.69671	+	4.67084i	−0.0948699	+	0.164319i
$809$	2.70877	−	4.69173i	0.0952353	−	0.164952i	−0.814471	−	0.580204i	$-0.802973\pi$
$809$	2.70877	−	4.69173i	0.0952353	−	0.164952i	0.909707	+	0.415251i	$0.136306\pi$
$810$	−1.26426	−	2.18976i	−0.0444216	−	0.0769404i
$811$	42.4931			1.49213			0.746067	−	0.665871i	$-0.231940\pi$
$811$	42.4931			1.49213			0.746067	+	0.665871i	$0.231940\pi$
$812$	9.89356	−	7.11771i	0.347196	−	0.249783i
$813$	−9.37763			−0.328888
$814$	−19.4518	−	33.6915i	−0.681785	−	1.18089i
$815$	−15.4928	+	26.8343i	−0.542688	+	0.939964i
$816$	3.41196	−	5.90969i	0.119442	−	0.206880i
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$	0.369291			0.0129120
$819$	0.103964	+	1.03568i	0.00363281	+	0.0361895i
$820$	−7.72979			−0.269936
$821$	−26.0134	−	45.0565i	−0.907874	−	1.57248i	−0.817012	−	0.576621i	$-0.804371\pi$
$821$	−26.0134	−	45.0565i	−0.907874	−	1.57248i	−0.0908625	−	0.995863i	$-0.528962\pi$
$822$	−8.76440	+	15.1804i	−0.305694	+	0.529477i
$823$	−20.2016	+	34.9901i	−0.704182	+	1.21968i	0.262804	+	0.964849i	$0.415353\pi$
$823$	−20.2016	+	34.9901i	−0.704182	+	1.21968i	−0.966986	+	0.254830i	$0.917981\pi$
$824$	9.07558	+	15.7194i	0.316163	+	0.547610i
$825$	−5.98528			−0.208381
$826$	−24.3948	−	10.9981i	−0.848802	−	0.382673i
$827$	1.31040			0.0455670			0.0227835	−	0.999740i	$-0.492747\pi$
$827$	1.31040			0.0455670			0.0227835	+	0.999740i	$0.492747\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−10.7042	+	18.5402i	−0.371773	+	0.643929i	−0.989838	−	0.142197i	$-0.954583\pi$
$829$	−10.7042	+	18.5402i	−0.371773	+	0.643929i	0.618066	+	0.786126i	$0.287917\pi$
$830$	17.2544	−	29.8855i	0.598910	−	1.03734i
$831$	−5.96359	−	10.3292i	−0.206875	−	0.358317i
$832$	0.393417			0.0136393
$833$	−46.8144	+	9.49441i	−1.62202	+	0.328962i
$834$	−13.0413			−0.451582
$835$	−6.09342	−	10.5541i	−0.210871	−	0.365240i
$836$	4.29540	−	7.43985i	0.148560	−	0.257313i
$837$	−1.00000	+	1.73205i	−0.0345651	+	0.0598684i
$838$	−15.2418	−	26.3996i	−0.526520	−	0.911960i
$839$	−43.5238			−1.50261			−0.751305	−	0.659955i	$-0.770575\pi$
$839$	−43.5238			−1.50261			−0.751305	+	0.659955i	$0.770575\pi$
$840$	6.09869	+	2.74952i	0.210425	+	0.0948676i
$841$	−7.77939			−0.268255
$842$	−17.1477	−	29.7007i	−0.590949	−	1.02355i
$843$	−5.33914	+	9.24765i	−0.183890	+	0.318506i
$844$	−7.59869	+	13.1613i	−0.261558	+	0.453031i
$845$	16.2397	+	28.1280i	0.558663	+	0.967632i
$846$	−9.59080			−0.329738
$847$	1.96886	+	19.6135i	0.0676509	+	0.673927i
$848$	0.258313			0.00887051
$849$	−5.61670	−	9.72841i	−0.192765	−	0.333878i
$850$	−4.75428	+	8.23466i	−0.163071	+	0.282446i
$851$	4.52852	−	7.84363i	0.155236	−	0.268876i
$852$	−6.93050	−	12.0040i	−0.237435	−	0.411250i
$853$	41.2137			1.41113			0.705566	−	0.708645i	$-0.250693\pi$
$853$	41.2137			1.41113			0.705566	+	0.708645i	$0.250693\pi$
$854$	6.90092	−	4.96472i	0.236145	−	0.169889i
$855$	−5.05704			−0.172947
$856$	−8.29540	−	14.3681i	−0.283531	−	0.491090i
$857$	−13.7459	+	23.8085i	−0.469550	+	0.813284i	−0.999394	−	0.0348112i	$-0.988917\pi$
$857$	−13.7459	+	23.8085i	−0.469550	+	0.813284i	0.529844	+	0.848095i	$0.322250\pi$
$858$	0.844941	−	1.46348i	0.0288458	−	0.0499624i
$859$	−1.52063	−	2.63381i	−0.0518832	−	0.0898643i	0.838917	−	0.544259i	$-0.183189\pi$
$859$	−1.52063	−	2.63381i	−0.0518832	−	0.0898643i	−0.890801	+	0.454394i	$0.849856\pi$
$860$	5.05704			0.172444
$861$	6.56561	−	4.72349i	0.223755	−	0.160976i
$862$	32.1966			1.09662
$863$	−4.85244	−	8.40467i	−0.165179	−	0.286098i	0.771540	−	0.636181i	$-0.219487\pi$
$863$	−4.85244	−	8.40467i	−0.165179	−	0.286098i	−0.936719	+	0.350083i	$0.886154\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−29.0265	+	50.2754i	−0.986932	+	1.70942i
$866$	11.2796	+	19.5369i	0.383297	+	0.663890i
$867$	−29.5659			−1.00411
$868$	−0.528521	−	5.26504i	−0.0179392	−	0.178707i
$869$	15.9127			0.539803
$870$	5.82392	+	10.0873i	0.197449	+	0.341992i
$871$	−0.736021	+	1.27483i	−0.0249391	+	0.0431958i
$872$	−7.28280	+	12.6142i	−0.246627	+	0.427170i
$873$	4.00000	+	6.92820i	0.135379	+	0.234484i
$874$	2.00000			0.0676510
$875$	21.9954	+	9.91639i	0.743581	+	0.335235i
$876$	−4.21317			−0.142350
$877$	−1.48794	−	2.57718i	−0.0502441	−	0.0870253i	0.839810	−	0.542881i	$-0.182667\pi$
$877$	−1.48794	−	2.57718i	−0.0502441	−	0.0870253i	−0.890054	+	0.455856i	$0.849333\pi$
$878$	−2.97481	+	5.15252i	−0.100395	+	0.173889i
$879$	11.0882	−	19.2053i	0.373995	−	0.647778i
$880$	−5.43050	−	9.40591i	−0.183062	−	0.317073i
$881$	−26.9064			−0.906501			−0.453250	−	0.891383i	$-0.649736\pi$
$881$	−26.9064			−0.906501			−0.453250	+	0.891383i	$0.649736\pi$
$882$	−6.86033	+	1.39134i	−0.230999	+	0.0468489i
$883$	19.9159			0.670224			0.335112	−	0.942178i	$-0.391226\pi$
$883$	19.9159			0.670224			0.335112	+	0.942178i	$0.391226\pi$
$884$	−1.34232	−	2.32497i	−0.0451472	−	0.0781972i
$885$	12.7868	−	22.1474i	0.429825	−	0.744478i
$886$	−7.62197	+	13.2016i	−0.256065	+	0.443518i
$887$	−8.60393	−	14.9024i	−0.288892	−	0.500375i	0.684654	−	0.728868i	$-0.259953\pi$
$887$	−8.60393	−	14.9024i	−0.288892	−	0.500375i	−0.973545	+	0.228493i	$0.926620\pi$
$888$	−9.05704			−0.303934
$889$	−15.1235	−	6.81825i	−0.507226	−	0.228677i
$890$	−20.9114			−0.700951
$891$	−2.14770	−	3.71993i	−0.0719507	−	0.124622i
$892$	10.5856	−	18.3347i	0.354431	−	0.613892i
$893$	−9.59080	+	16.6118i	−0.320944	+	0.555891i
$894$	−0.0311393	−	0.0539349i	−0.00104145	−	0.00180385i
$895$	55.2361			1.84634
$896$	0.264260	+	2.63252i	0.00882832	+	0.0879464i
$897$	0.393417			0.0131358
$898$	11.2744	+	19.5278i	0.376231	+	0.651651i
$899$	4.60658	−	7.97884i	0.153638	−	0.266109i
$900$	−0.696708	+	1.20673i	−0.0232236	+	0.0402245i
$901$	−0.881354	−	1.52655i	−0.0293622	−	0.0508567i
$902$	−13.1312			−0.437222
$903$	−4.29540	+	3.09023i	−0.142942	+	0.102837i
$904$	−9.11932			−0.303304
$905$	27.9394	+	48.3924i	0.928735	+	1.60862i
$906$	−1.07806	+	1.86726i	−0.0358162	+	0.0620355i
$907$	7.96886	−	13.8025i	0.264602	−	0.458304i	−0.702858	−	0.711331i	$-0.748093\pi$
$907$	7.96886	−	13.8025i	0.264602	−	0.458304i	0.967459	+	0.253027i	$0.0814262\pi$
$908$	1.20474	+	2.08667i	0.0399807	+	0.0692487i
$909$	5.39342			0.178888
$910$	2.13645	−	1.53702i	0.0708227	−	0.0509519i
$911$	−30.6965			−1.01702			−0.508511	−	0.861056i	$-0.669804\pi$
$911$	−30.6965			−1.01702			−0.508511	+	0.861056i	$0.669804\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	29.3115	−	50.7689i	0.970068	−	1.68021i
$914$	−1.05704	+	1.83085i	−0.0349638	+	0.0605591i
$915$	4.06228	+	7.03607i	0.134295	+	0.232605i
$916$	10.6160			0.350762
$917$	−5.04692	−	50.2767i	−0.166664	−	1.66028i
$918$	−6.82392			−0.225223
$919$	−1.33390	−	2.31038i	−0.0440012	−	0.0762124i	0.843186	−	0.537622i	$-0.180677\pi$
$919$	−1.33390	−	2.31038i	−0.0440012	−	0.0762124i	−0.887187	+	0.461410i	$0.847344\pi$
$920$	1.26426	−	2.18976i	0.0416814	−	0.0721944i
$921$	−4.00789	+	6.94187i	−0.132065	+	0.228742i
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	−5.45315			−0.179493
$924$	10.3603	+	4.67084i	0.340830	+	0.153659i
$925$	12.6202			0.414951
$926$	1.21317	+	2.10127i	0.0398671	+	0.0690519i
$927$	9.07558	−	15.7194i	0.298081	−	0.516292i
$928$	−2.30329	+	3.98942i	−0.0756092	+	0.130959i
$929$	−23.4770	−	40.6634i	−0.770255	−	1.33412i	−0.937423	−	0.348193i	$-0.886795\pi$
$929$	−23.4770	−	40.6634i	−0.770255	−	1.33412i	0.167168	−	0.985928i	$-0.446538\pi$
$930$	5.05704			0.165827
$931$	−4.45046	+	13.2738i	−0.145858	+	0.435031i
$932$	13.1816			0.431778
$933$	10.7954	+	18.6982i	0.353426	+	0.612151i
$934$	9.89356	−	17.1361i	0.323727	−	0.560712i
$935$	−37.0573	+	64.1852i	−1.21190	+	2.09908i
$936$	−0.196708	−	0.340709i	−0.00642962	−	0.0111364i
$937$	11.9895			0.391681			0.195840	−	0.980636i	$-0.437257\pi$
$937$	11.9895			0.391681			0.195840	+	0.980636i	$0.437257\pi$
$938$	−9.02480	−	4.06873i	−0.294670	−	0.132849i
$939$	−13.1816			−0.430165
$940$	12.1253	+	21.0016i	0.395483	+	0.684996i
$941$	−17.4466	+	30.2183i	−0.568742	+	0.985090i	0.427949	+	0.903803i	$0.359236\pi$
$941$	−17.4466	+	30.2183i	−0.568742	+	0.985090i	−0.996691	+	0.0812869i	$0.974097\pi$
$942$	5.54112	−	9.59750i	0.180539	−	0.312703i
$943$	−1.52852	−	2.64748i	−0.0497755	−	0.0862137i
$944$	10.1141			0.329185
$945$	−0.668188	−	6.65638i	−0.0217361	−	0.216532i
$946$	8.59080			0.279311
$947$	8.75708	+	15.1677i	0.284567	+	0.492884i	0.972504	−	0.232886i	$-0.0748169\pi$
$947$	8.75708	+	15.1677i	0.284567	+	0.492884i	−0.687937	+	0.725770i	$0.741484\pi$
$948$	1.85230	−	3.20828i	0.0601599	−	0.104200i
$949$	−0.828765	+	1.43546i	−0.0269029	+	0.0465971i
$950$	1.39342	+	2.41347i	0.0452084	+	0.0783033i
$951$	14.2282			0.461380
$952$	14.6557	−	10.5438i	0.474995	−	0.341725i
$953$	−13.3209			−0.431505			−0.215753	−	0.976448i	$-0.569221\pi$
$953$	−13.3209			−0.431505			−0.215753	+	0.976448i	$0.569221\pi$
$954$	−0.129157	−	0.223706i	−0.00418160	−	0.00724274i
$955$	10.4557	−	18.1098i	0.338338	−	0.586019i
$956$	−2.12721	+	3.68444i	−0.0687989	+	0.119163i
$957$	9.89356	+	17.1361i	0.319813	+	0.553933i
$958$	22.1246			0.714812
$959$	−37.6466	+	27.0840i	−1.21567	+	0.874589i
$960$	−2.52852			−0.0816077
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−1.78160	+	3.08582i	−0.0574410	+	0.0994907i
$963$	−8.29540	+	14.3681i	−0.267316	+	0.463004i
$964$	−7.76688	−	13.4526i	−0.250154	−	0.433280i
$965$	−16.4543			−0.529684
$966$	0.264260	+	2.63252i	0.00850244	+	0.0847000i
$967$	−61.9397			−1.99185			−0.995923	−	0.0902039i	$-0.971248\pi$
$967$	−61.9397			−1.99185			−0.995923	+	0.0902039i	$0.971248\pi$
$968$	−3.72523	−	6.45229i	−0.119733	−	0.207384i
$969$	−6.82392	+	11.8194i	−0.219216	+	0.379693i
$970$	10.1141	−	17.5181i	0.324744	−	0.562472i
$971$	−3.57297	−	6.18856i	−0.114662	−	0.198600i	0.802983	−	0.596002i	$-0.203245\pi$
$971$	−3.57297	−	6.18856i	−0.114662	−	0.198600i	−0.917645	+	0.397402i	$0.869912\pi$
$972$	−1.00000			−0.0320750
$973$	−31.4550	−	14.1811i	−1.00840	−	0.454626i
$974$	8.54876			0.273920
$975$	0.274097	+	0.474750i	0.00877813	+	0.0152042i
$976$	−1.60658	+	2.78268i	−0.0514255	+	0.0890715i
$977$	12.1662	−	21.0726i	0.389233	−	0.674171i	−0.603114	−	0.797655i	$-0.706074\pi$
$977$	12.1662	−	21.0726i	0.389233	−	0.674171i	0.992347	+	0.123484i	$0.0394069\pi$
$978$	6.12721	+	10.6126i	0.195927	+	0.339355i
$979$	−35.5238			−1.13535
$980$	11.7200	+	13.2635i	0.374380	+	0.423687i
$981$	14.5656			0.465044
$982$	−11.2180	−	19.4302i	−0.357981	−	0.620041i
$983$	18.0781	−	31.3121i	0.576601	−	0.998702i	−0.419265	−	0.907864i	$-0.637712\pi$
$983$	18.0781	−	31.3121i	0.576601	−	0.998702i	0.995866	−	0.0908377i	$-0.0289545\pi$
$984$	−1.52852	+	2.64748i	−0.0487275	+	0.0843984i
$985$	−10.3420	−	17.9128i	−0.329522	−	0.570750i
$986$	31.4350			1.00109
$987$	−23.1326	−	10.4291i	−0.736320	−	0.331961i
$988$	−0.786834			−0.0250325
$989$	1.00000	+	1.73205i	0.0317982	+	0.0550760i
$990$	−5.43050	+	9.40591i	−0.172593	+	0.298939i
$991$	1.88620	−	3.26699i	0.0599171	−	0.103779i	−0.834511	−	0.550991i	$-0.814250\pi$
$991$	1.88620	−	3.26699i	0.0599171	−	0.103779i	0.894428	+	0.447212i	$0.147583\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$	21.5975			0.685375
$994$	−3.66291	−	36.4894i	−0.116181	−	1.15737i
$995$	−36.4347			−1.15506
$996$	−6.82392	−	11.8194i	−0.216224	−	0.374511i
$997$	16.6321	−	28.8076i	0.526743	−	0.912345i	−0.472772	−	0.881185i	$-0.656747\pi$
$997$	16.6321	−	28.8076i	0.526743	−	0.912345i	0.999514	−	0.0311600i	$-0.00992013\pi$
$998$	18.2465	−	31.6039i	0.577584	−	1.00040i
$999$	4.52852	+	7.84363i	0.143276	+	0.248161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.m.277.2	✓	8
7.2	even	3	inner	966.2.i.m.415.2	yes	8
7.3	odd	6		6762.2.a.cr.1.2		4
7.4	even	3		6762.2.a.cl.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.2	✓	8	1.1	even	1	trivial
966.2.i.m.415.2	yes	8	7.2	even	3	inner
6762.2.a.cl.1.3		4	7.4	even	3
6762.2.a.cr.1.2		4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.26426 - 2.18976i) q^{5} -1.00000 q^{6} +(-2.41196 - 1.08740i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.26426 - 2.18976i) q^{5} -1.00000 q^{6} +(-2.41196 - 1.08740i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.26426 + 2.18976i) q^{10} +(-2.14770 + 3.71993i) q^{11} +(0.500000 + 0.866025i) q^{12} +0.393417 q^{13} +(0.264260 + 2.63252i) q^{14} -2.52852 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.41196 + 5.90969i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +2.52852 q^{20} +(-2.14770 + 1.54512i) q^{21} +4.29540 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.696708 + 1.20673i) q^{25} +(-0.196708 - 0.340709i) q^{26} -1.00000 q^{27} +(2.14770 - 1.54512i) q^{28} +4.60658 q^{29} +(1.26426 + 2.18976i) q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.14770 + 3.71993i) q^{33} +6.82392 q^{34} +(0.668188 + 6.65638i) q^{35} +1.00000 q^{36} +(-4.52852 - 7.84363i) q^{37} +(1.00000 - 1.73205i) q^{38} +(0.196708 - 0.340709i) q^{39} +(-1.26426 - 2.18976i) q^{40} -3.05704 q^{41} +(2.41196 + 1.08740i) q^{42} +2.00000 q^{43} +(-2.14770 - 3.71993i) q^{44} +(-1.26426 + 2.18976i) q^{45} +(0.500000 - 0.866025i) q^{46} +(4.79540 + 8.30588i) q^{47} -1.00000 q^{48} +(4.63510 + 5.24555i) q^{49} +1.39342 q^{50} +(3.41196 + 5.90969i) q^{51} +(-0.196708 + 0.340709i) q^{52} +(-0.129157 + 0.223706i) q^{53} +(0.500000 + 0.866025i) q^{54} +10.8610 q^{55} +(-2.41196 - 1.08740i) q^{56} +2.00000 q^{57} +(-2.30329 - 3.98942i) q^{58} +(-5.05704 + 8.75905i) q^{59} +(1.26426 - 2.18976i) q^{60} +(-1.60658 - 2.78268i) q^{61} -2.00000 q^{62} +(0.264260 + 2.63252i) q^{63} +1.00000 q^{64} +(-0.497381 - 0.861490i) q^{65} +(2.14770 - 3.71993i) q^{66} +(-1.87084 + 3.24040i) q^{67} +(-3.41196 - 5.90969i) q^{68} +1.00000 q^{69} +(5.43050 - 3.90686i) q^{70} -13.8610 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-2.10658 + 3.64871i) q^{73} +(-4.52852 + 7.84363i) q^{74} +(0.696708 + 1.20673i) q^{75} -2.00000 q^{76} +(9.22523 - 6.63689i) q^{77} -0.393417 q^{78} +(-1.85230 - 3.20828i) q^{79} +(-1.26426 + 2.18976i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.52852 + 2.64748i) q^{82} -13.6478 q^{83} +(-0.264260 - 2.63252i) q^{84} +17.2544 q^{85} +(-1.00000 - 1.73205i) q^{86} +(2.30329 - 3.98942i) q^{87} +(-2.14770 + 3.71993i) q^{88} +(4.13510 + 7.16221i) q^{89} +2.52852 q^{90} +(-0.948906 - 0.427803i) q^{91} -1.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(4.79540 - 8.30588i) q^{94} +(2.52852 - 4.37953i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(2.22523 - 6.63689i) q^{98} +4.29540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

Introduction

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